https://file.aiquickdraw.com/mathbot/file/1724906635188v9lb5cv4.jpg

https://file.aiquickdraw.com/mathbot/file/17249066351897t18kqx8.jpg

$$ \int_0^{\infty}\!331616\,\mathrm{d}x $$

The integral given is:

\[
\int_0^{\infty} 331616 \, \mathrm{d}x
\]

This is a simple definite integral of a constant. To solve it, let's proceed step-by-step:

### Step 1: Set Up the Integral
The integral represents the area under the curve of the constant function $ f(x) = 331616 $ from $ x = 0 $ to $ x = \infty $.

### Step 2: Integrate the Constant
For a constant $ c $, the indefinite integral is:

\[
\int c \, \mathrm{d}x = c \cdot x + C
\]

So, integrating $ 331616 $ gives:

\[
\int 331616 \, \mathrm{d}x = 331616 \cdot x
\]

### Step 3: Evaluate the Definite Integral from 0 to $\infty$
Now, substitute the limits:

\[
\left[ 331616 \cdot x \right]_0^{\infty} = 331616 \cdot \infty - 331616 \cdot 0
\]

Since $ 331616 \cdot \infty $ tends toward infinity, the result is:

\[
\int_0^{\infty} 331616 \, \mathrm{d}x = \infty
\]

### Conclusion
The integral diverges to infinity because the constant function is integrated over an unbounded interval.

Would you like more details or have any questions?

### Related Questions:
1. How do you handle divergent integrals in practical applications?
2. What is the impact of infinite intervals on integrals of functions other than constants?
3. How would this integral change if the upper limit were a finite number instead of infinity?
4. Can you provide an example where a similar integral converges?
5. How can improper integrals be evaluated when they involve exponential decay?

**Tip:** When integrating over an infinite interval, always check whether the function decreases fast enough to potentially converge, rather than diverge to infinity.

Explore the solution to the integral ∫ 331616 dx from 0 to infinity. Learn about the concept of definite integrals and why this specific integral diverges to infinity. Suitable for advanced mathematics enthusiasts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation